"We have seen the foreign minister and the immigration minister flat out deny it and then the prime minister seems to indicate that this may have happened," she said in Sydney.

"It is absolutely vital that the prime minister does what he has to do to get this relationship back on track."

Mr Abbott skirted the allegations at a Sydney Liberal Party function on Saturday.

He instead made a dig at opposition leader Bill Shorten, and claims the former Labor government had also paid-off people smugglers.

"On Monday, Mr Shorten attacked us for allegedly doing something to turn around boats, which it turned out he tried to do exactly the same - only it didn't work when he tried to do it," Mr Abbott said.

Indonesia's foreign affairs ministry claims to have evidence Australian officials paid the crew to turn their boat around, and has demanded an explanation from Australia.

Indonesian vice-president Jusuf Kalla has said the payments would amount to bribery and possibly even people-trafficking.

In other developments, Australia's top medical organisations have called for urgent amendments to the Border Force Act, so they can freely speak about the healthcare problems detainees face at immigration centres.

They have released a joint statement, saying it is "inconceivable" they could face up to two years' jail for sharing information about conditions at the centres.